The present work employs the single relaxation time lattice Boltzmann method along with the pseudo potential model for the two-phase flow simulation of a ferrofluid in a random two-dimensional medium under the influence of a spatially variable external magnetic field. The magnetic field is created and controlled by placing a permanent magnet at the outlet end of the channel filled with a porous medium. The magnitude of the magnetic force acting on the ferrofluid is controlled by changing the distance of the magnet from the channel outlet. The spatially variable magnetic field strength was analytically calculated inside the channel using the available relations in the literature. The main goal of the present work is to qualitatively study the applicability of the single relaxation time (SRT) lattice Boltzmann method (LBM) to modelling flow of a ferrofluid and its steering into porous media. Penetration of the ferrofluid into the porous medium, which is initially filled with a fluid with no magnetic properties, was simulated in time. The simulation results for the flow front are presented and the effect of the magnetic field strength on the rate of flow penetration and front advancement was studied qualitatively. The LBM has proved to be a powerful tool for modelling flows, which involve multi-physics in complex geometries, when mesoscopic inter-particle forces and interaction with external complex forces have to be determined.

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